Differential Equations

Runge-Kutta (RK4) — Numerical ODE Solver

4th-order method: yₙ₊₁ = yₙ + (h/6)(k₁ + 2k₂ + 2k₃ + k₄). Each step uses four slope estimates for superior accuracy. Compare against Euler and the exact solution.

Live Calculator · Step-by-Step · Differential Equations

Inputs

f(x, y) = dy/dx

x₀

y₀

x_end

Step size h

Result

RK4 Formula

yₙ₊₁ = yₙ + (h/6)(k₁+2k₂+2k₃+k₄)

RK4 Approx y(x_end)

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Exact y(x_end)

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RK4 Error

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RK4 Iteration Table

Configure inputs above.

RK4 vs Euler vs Exact